### Abstract

It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the whole complex plane. In this paper, the case of specific (nonreal analytic) smooth functions is precisely investigated. Indeed, asymptotic limits of the respective local zeta functions at some singularities in one direction are explicitly computed. Surprisingly, it follows from these behaviors that these local zeta functions have singularities different from poles.

Original language | English |
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Pages (from-to) | 661-676 |

Number of pages | 16 |

Journal | Transactions of the American Mathematical Society |

Volume | 372 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2019 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*372*(1), 661-676. https://doi.org/10.1090/tran/7771

**Nonpolar singularities of local zeta functions in some smooth case.** / Kamimoto, Joe; Nose, Toshihiro.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 372, no. 1, pp. 661-676. https://doi.org/10.1090/tran/7771

}

TY - JOUR

T1 - Nonpolar singularities of local zeta functions in some smooth case

AU - Kamimoto, Joe

AU - Nose, Toshihiro

PY - 2019/1/1

Y1 - 2019/1/1

N2 - It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the whole complex plane. In this paper, the case of specific (nonreal analytic) smooth functions is precisely investigated. Indeed, asymptotic limits of the respective local zeta functions at some singularities in one direction are explicitly computed. Surprisingly, it follows from these behaviors that these local zeta functions have singularities different from poles.

AB - It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the whole complex plane. In this paper, the case of specific (nonreal analytic) smooth functions is precisely investigated. Indeed, asymptotic limits of the respective local zeta functions at some singularities in one direction are explicitly computed. Surprisingly, it follows from these behaviors that these local zeta functions have singularities different from poles.

UR - http://www.scopus.com/inward/record.url?scp=85070261388&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85070261388&partnerID=8YFLogxK

U2 - 10.1090/tran/7771

DO - 10.1090/tran/7771

M3 - Article

AN - SCOPUS:85070261388

VL - 372

SP - 661

EP - 676

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 1

ER -